Jenkins played the majority of his career for the Cubs. He was a National League (NL) and Cubs All-Star for three seasons, and in 1971, he was the first Canadian and Cubs pitcher to win a Cy Young Award. He was a 20-game winner for seven seasons, including six consecutive seasons for the Cubs. He was the NL leader in wins, in 1971, and the American League (AL) leader in wins, in 1974. He was also the NL leader in complete games in 1967, 1970, and 1971, and the AL leader in complete games in 1974. He led the NL in strikeouts in 1969 and had over 3,000 strikeouts during his career.

A talented athlete, Jenkins competed in track and field, ice hockey, and basketball in his school years, lettering five times. When he began playing bantam baseball in his teens, he started out as a first baseman. He honed his pitching skills by throwing pieces of coal from a local coal yard, aiming at either an open ice chute or the gaps of passing boxcars.[2] He was also encouraged to continue working on his pitching by Gene Dziadura, a former shortstop in the Chicago Cubs minor league system, and a Philadelphia Phillies scout. Many training sessions between the two followed until Jenkins graduated from high school.

In 1962, Jenkins was signed by Philadelphia Phillies scout Tony Lucadello.[2] Jenkins made his major-league debut as a 22-year-old in 1965, as a relief pitcher. He was traded the following year to the Chicago Cubs, along with Adolfo Phillips and John Herrnstein, for pitchers Larry Jackson and Bob Buhl. Jenkins would become one of the best pitchers in the majors. In his first full year as a starter for the Cubs (1967), Jenkins recorded twenty wins while posting a 2.80 ERA and 236 strikeouts. He finished tied for second in the Cy Young Award voting, following Mike McCormick of the San Francisco Giants. He was also selected for the All-Star Game for the first time that season.

The following year his numbers improved; once again he won twenty games, his ERA dropped to 2.63 and his strikeout total increased to 260. Jenkins established a reputation for achieving his pitching feats and his statistics while spending most of his career pitching in a "hitter's ballpark"—Wrigley Field in Chicago.[6] Furthermore, in 1968, Jenkins lost five of his starts in 1–0 ballgames.

Jenkins had his best season in 1971. On April 6, 1971, Jenkins started the Cubs' opening-day game. The Cubs defeated the St. Louis Cardinals 2–1 in 10 innings at Wrigley Field. Jenkins pitched a complete game for the Cubs, and Billy Williams hit a home run in the final inning for the victory.[7] On September 1, 1971, Jenkins threw another complete game against the Montreal Expos and had two home runs. The Cubs won the game 5–2.[8] He was named NL Player of the Month (for the only time in his career) in July, with a 6-1 record, a 2.14 ERA, and 49 strikeouts.

That season, Jenkins threw a complete game in 30 of 39 starts and received a decision in 37 of them, finishing with a 24–13 record (.649). He walked only 37 batters versus 263 strikeouts across 325 innings.[9] He played in the All-Star Game and finished seventh in MVP voting. Jenkins also posted a .478 slugging percentage, hitting six home runs and driving in twenty runs in just 115 at-bats.

Jenkins won the 1971 NL Cy Young Award. Jenkins was the first Cubs pitcher and the first Canadian to win the Cy Young Award (Quebec native Éric Gagné is the only other Canadian to match the feat). He received 17 of 24 first-place votes. He was outpitched in several statistical categories by New York Mets pitcher Tom Seaver, but Jenkins pitched in hitter-friendly Wrigley Field and Seaver worked in pitcher-friendly Shea Stadium.

In 1972, Jenkins completed his sixth consecutive season with 20 or more wins.[10] By the middle of the following season, Jenkins expressed that he did not feel like playing baseball anymore. Jenkins finished the season, but registered a 14–16 win-loss record.

After that season, Jenkins was traded to the Texas Rangers. Texas manager Billy Martin was pleased with the trade, describing Jenkins as a workhorse and a winner.[11] In 1974, Jenkins achieved a personal best 25 wins during the season, setting a Rangers franchise record which still stands. He finished second in Cy Young Award voting for the second time in his career behind Catfish Hunter in a very close vote (90 points to Jenkins's 75); surprisingly, Jenkins actually finished ahead of Hunter in MVP voting (118 points to Hunter's 107), and his fifth-place finish on the MVP leader-board was the highest of his career. He was named AL Comeback Player of the Year.

Jenkins achieved his 250th win against the Oakland Athletics on May 23, 1980. Later that year, during a customs search in Toronto, Jenkins was found possessing 3.0 grams cocaine, 2.2 grams hashish, and 1.75 grams marijuana. In response, on September 8, CommissionerBowie Kuhn suspended him indefinitely. However, Jenkins' suspension lasted only two weeks before, in an unprecedented action, an independent arbiter, Raymond Goetz, overturned the suspension and reinstated him and he returned to the league. Eventually, when he went to trial, the judge gave him an absolute discharge for lack of some evidence.[12] Jenkins was not further punished by MLB for the incident, as he remained active until his retirement following the 1983 season. It has been suggested that this incident delayed his induction into the Baseball Hall of Fame.[13]

Jenkins led the league in wins twice, (1971, 1974) fewest walks per 9 innings five times, complete games nine times, and home runs allowed seven times. He led the league in strikeouts once (1969, with 273). His streak of six straight seasons with 20 or more wins (1967–1972) is the longest streak in the major leagues since Warren Spahn performed the feat between 1956 and 1961.

On December 17, 1979, he was made a Member of the Order of Canada for being "Canada's best-known major-league baseball player".[20] Governor General Michaëlle Jean officiated at his investiture into the Order, which finally occurred on May 4, 2007: over 27 years after he was appointed.[21] On May 3, 2009, the Cubs retired jersey number 31 in honor of both Jenkins and Greg Maddux.[22] On December 13, 2010, Canada Post announced that Jenkins would be honoured in Canada with his own postage stamp. The stamp would be issued in February 2011 to commemorate Black History Month.[23]